# Math Help - A^-1 and a proof help

1. ## A^-1 and a proof help

Hello guys, I've been trying to solve this problem all night and was wondering if I could get some help.

1. Suppose A is nxn nonsingular. Prove Det(A^-1) = 1 / Det(A)
I was trying to use the formula A^-1 = 1 / det(A) * adj(A) but had no luck

2. A = | 1/2 -1/2 | find A^-1
| 1/2x 1/2x|

I keep getting
1 1/x
-1 x

2. Originally Posted by sleepiiee
Hello guys, I've been trying to solve this problem all night and was wondering if I could get some help.

1. Suppose A is nxn nonsingular. Prove Det(A^-1) = 1 / Det(A)
I was trying to use the formula A^-1 = 1 / det(A) * adj(A) but had no luck

2. A = | 1/2 -1/2 | find A^-1
| 1/2x 1/2x|

I keep getting
1 1/x
-1 x

$AA^{-1} = I$

$\det{(AA^{-1})} = \det{(I)}$

$\det{(A)}\det{(A^{-1})} = 1$

$\det{(A^{-1})} = \frac{1}{\det{(A)}}$.